To determine the probability that a randomly selected student received a B, we'll follow these steps:
1. Identify the Known Probabilities:
The probabilities provided in the table are:
- Grade A (4): [tex]\( \text{P}(A) = 0.43 \)[/tex]
- Grade C (2): [tex]\( \text{P}(C) = 0.17 \)[/tex]
- Grade D (1): [tex]\( \text{P}(D) = 0.05 \)[/tex]
- Grade F (0): [tex]\( \text{P}(F) = 0.04 \)[/tex]
2. Understand the Total Probability Requirement:
The total probability of all possible outcomes must sum up to 1. That is:
[tex]\[
\text{P}(A) + \text{P}(B) + \text{P}(C) + \text{P}(D) + \text{P}(F) = 1
\][/tex]
3. Form the Equation:
We do not yet know [tex]\( \text{P}(B) \)[/tex]. We can represent it as [tex]\( x \)[/tex]. Plugging in the known values, we get:
[tex]\[
0.43 + x + 0.17 + 0.05 + 0.04 = 1
\][/tex]
4. Simplify the Equation:
First, combine the known probabilities:
[tex]\[
0.43 + 0.17 + 0.05 + 0.04 = 0.69
\][/tex]
So, the equation reduces to:
[tex]\[
0.69 + x = 1
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 1 - 0.69 = 0.31
\][/tex]
6. Conclusion:
The probability that a randomly selected student got a B is [tex]\( \text{P}(B) = 0.31 \)[/tex].
Hence, the correct option is:
[tex]\[ \boxed{0.31} \][/tex]
